A formal proof that compiles without errors is not the end of the story. The harder and more consequential challenges lie in what comes next: organizing, integrating, and maintaining formal knowledge at a planetary scale. These are challenges that the world will confront over the coming years as an increasing number of proofs are produced by AI systems. The ability to integrate these proofs into an ever-expanding, intercompatible knowledge base will soon be a basic requirement for scale. We will continue to collaborate with the maintainers of the sphere packing project and other libraries of formal mathematics to ensure the code Gauss has produced remains usable and maintainable for posterity. As a first step in that direction, we used Gauss to automatically refactor, optimize, and improve the style of the formalization it produced, effectively decreasing its size from 500,000 lines at peak to the released version of ~200,000 lines.
If you placed the MacBook Air M4 and the M5 in front of me, I wouldn’t be able to tell which was which. The M5 offers an overall CPU/GPU performance boost, along with some extra storage and double the file transfer speeds. Still, I didn’t expect a radical change, but I wish we got more for that extra $100.
。关于这个话题，91视频提供了深入分析
한동훈 “나를 탄핵의 바다 건너는 배로 써달라…출마는 부수적 문제”
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Одному из российских рынков предсказали рост до полутриллиона рублей15:00